Comprehensive hierarchical data structures: binary trees, traversals, BST, AVL self-balancing, Red-Black trees, Splay, Heaps, B-Trees, and Tries.
Hierarchical terminology, mathematical relationship between edges and nodes (E = V - 1), full vs complete vs perfect binary trees.
Preorder, Inorder, Postorder recursive and iterative patterns, Level-order BFS, and Morris Inorder O(1) space threading.
BST ordering invariant, search and insertion mechanics, and the 3-case deletion algorithm (no child, 1 child, 2 children).
Height-balance factor BF in {-1, 0, 1}, and the 4 fundamental rotation algorithms: Left-Left, Right-Right, Left-Right, and Right-Left.
The 5 fundamental RBT invariants, black-height mathematical proof, 3-case insertion recoloring/rotations, and 4-case deletion handling.
Splay tree self-adjusting zig/zig-zig/zig-zag rotations, amortized O(log n) potential method, and Treap dual heap-priority invariants.
Array representation of complete binary trees, sift-up/down, mathematical proof of O(n) bottom-up Build-Heap, and D-ary heaps.
Storage page disk access latency, B-Tree (M-way) balancing invariants, proactive node splitting, and B+ Tree leaf linked-list sequential scans.
Standard prefix Trie node maps, prefix query matching, Radix / Patricia compressed edges, and Bitwise 0-1 Trie for maximum XOR queries.
Multi-dimensional spatial partitioning: Kd-Trees with k-NN bounding box pruning, Quadtrees, Cartesian trees, and Threaded Binary Trees.